[R] Looking for a test of standard normality

[Bert Gunter]

Well...

On Sun, Nov 11, 2012 at 6:12 PM, Herschtal Alan
<Alan.Herschtal at petermac.org> wrote:
> Thanks for your response. The background is that I am trying to test
> whether a small sample and a much larger sample actually came from the
> same distribution.

As this is logically impossible, I suggest you go back to basic
statistics texts and review the logic of statistical hypothesis
testing.  Then you should follow Rolf's advice and forget about
testing for normality. He told you why and provided references, IIRC.

-- Cheers,
Bert

 could just perform a KS test on the 2 samples, but
> as I said, ideally I'd like a test that is more powerful than that. So I
> look at the percentile ranks of the small sample within the large
> sample, which should be uniformly distributed if the 2 samples are from
> the same population, and then transform using "qnorm". The result should
> be standard normal. Perhaps the next best alternative is to do
> chi-square test on the percentiles, checking for equal numbers in each
> decile bin. This would certainly work, and the only disadvantage that I
> can see is that the selection of the bin boundaries is somewhat
> arbitrary.
>
> Alan Herschtal
> Senior Biostatistician
> Peter MacCallum Cancer Centre
>
> Phone +61 3 9656 3639
> Fax +61 3 9656 1420
> Email alan.herschtal at petermac.org
>
>
> -----Original Message-----
> From: Rolf Turner [mailto:rolf.turner at xtra.co.nz]
> Sent: Friday, 9 November 2012 2:17 PM
> To: Herschtal Alan
> Cc: r-help at r-project.org
> Subject: Re: [R] Looking for a test of standard normality
>
>
> Others may correct me, but I cannot imagine any test of standard
> normality
> giving appreciably more power than is given by the Kolmogorov-Smirnov
> test.
>
> I also wonder about the point of testing for (standard) normality in the
> first place.  There is a quote --- I think it refers to testing for
> heteroscedasticity,
> but I believe it applies equally to testing for normality  --- about
> such testing
> being analogous to going out of the harbour in a rowing dinghy to see if
>
> it's
> safe for an ocean liner to put to sea.
>
>      cheers,
>
>          Rolf Turner
>
> On 09/11/12 13:23, Herschtal Alan wrote:
>> Dear list members,
>>
>> I am looking for a goodness of test that will tell me if a sample is
>> likely to have come from a standard normal distribution. I can find
>> plenty of omnibus tests for normality in the nor.test package, but
> none
>> of them appear to allow me to test against the specific alternative
> that
>> the data are not standard normal. My back up option is to use a
>> Kolmogorov-Smirnov test, but my impression is that that is not a very
>> powerful test. Any suggestions?
>
> This email (including any attachments or links) may contain
> confidential and/or legally privileged information and is
> intended only to be read or used by the addressee.  If you
> are not the intended addressee, any use, distribution,
> disclosure or copying of this email is strictly
> prohibited.
> Confidentiality and legal privilege attached to this email
> (including any attachments) are not waived or lost by
> reason of its mistaken delivery to you.
> If you have received this email in error, please delete it
> and notify us immediately by telephone or email.  Peter
> MacCallum Cancer Centre provides no guarantee that this
> transmission is free of virus or that it has not been
> intercepted or altered and will not be liable for any delay
> in its receipt.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm